of them might be using a suboptimal approach to voting, perhaps in the aggregate the associated
errors cancel each other out. In short, perhaps Condorcet’s Jury Theorem restores optimality.
20
Condorcet’s Theorem does have this benign effect if voters are prospective and compare the
incumbent’s anticipated performance to the challenger’s. This comparison of alternatives to each
other is essential. If voters do this then their (independent) comparison or evaluation errors will
indeed cancel each other out: in the limit—i.e., in an infinitely large electorate—the party that
is better for the majority will win with probability one (Miller 1986). But in (pure) retrospective
voting, the incumbent is compared not to the challenger but to an internal standard: a voter’s
aspiration level. Poor performance, as measured by that standard, weakens support for the incum-
bent. The promises of the challenger are ignored. This makes it harder for the Jury Theorem to
help majority rule elections achieve the optimality standard. The next result reveals the problem
in the simple context of a homogeneous electorate; most of the logic carries over to heterogeneous
districts.
Part (iii) of this next result requires two new assumptions about how citizens adjust their
vote-propensities. First, propensity-adjustment cannot become arbitrarily sluggish in the face of
dissatisfaction; we call this (A2*), because it replaces the weaker negative feedback assumption of
(A2). Second, part (iii) also requires that AVoRs involve equal-adjustment: from any given current
vote-propensity in (0
, 1), positive and negative feedback produce changes of equal size (in absolute
value).
21
(A2*) (negative feedback):
If π
i,t
< a
i,t−1
then with probability one p
i,t
(I
t
)
≤ p
i,t−1
(W
t−1
),
and there exists an
> 0 such that for all t and for all histories leading up to t, if p
i,t−1
(W
t
− 1) > 0
then with probability one p
i,t
(I
t
)
≤ (1 − )p
i,t−1
(W
t−1
).
(A2*) says that when voters are dissatisfied, they will always decrease their propensity to vote
for the incumbent by a fixed percentage that is bounded away from zero.
20
For a thoughtful discussion of this topic, see Kinder (1998, p.797-800).
21
A simple type of equal-adjustment AVoR is a one-step walk along a finite grid of equally-spaced propensities,
e.g., (0
, 0.01, 0.02, . . . , 0.99, 1.0). But in other equal-adjustment AVoRs, propensity changes taper off as one moves
toward zero or one. And in nonstationary equal-adjustment rules the size of changes could decrease over time as a
person ages.
19
Convention